1. Technical Field
The present invention relates generally to the field of mathematical and empirical modeling. More specifically, the invention relates to a method and system for modeling the performance of a gas turbine engine.
2. Background Information
Early gas turbine engine models include piecewise linear state variable models (SVM) operable to describe reasonable behavior of an engine during steady state operation and mild transients. As processor speeds increased, more complex engine models that were a combination of linear and non-linear physics based elements were created. While the latter provided greater fidelity for transient operation over an engine's operational flight envelope, the accuracy required for long-term performance tracking as well as the need to address engine-to-engine variation was inadequate.
Modeling using physics-based principles is a crucial element in conditional based monitoring and engine health management for gas turbine engines. However, modern gas turbine engines have complex mechanical systems that are, practically speaking, difficult to accurately model and represent using physics-based principles. The modeling difficulties associated with engine complexity are exacerbated by noisy or inaccurate sensors, engine-to-engine variations, and complex modifications made to engines during their life time. Consequently, it is very difficult to model a gas turbine engine with high fidelity using only a physics-based model component.
FIG. 1 illustrates a schematic diagram of an engine model 101 used for performance tracking. The major components include the monitored engine 103, a physics-based engine model 105 and a performance estimation module 107. The physics-based engine model 105 is typically an SVM and the performance estimation module 107 can be a Kalman filter observer.
The engine model 101 is driven by a set of input parameters 109 that command the engine 103. The input parameters 109 comprise flight parameters such as Mach number, altitude, ambient conditions (e.g., temperature and pressure) and others, and power setting parameters such as engine pressure ratio (EPR), engine low rotor speed, fan pressure ratio (FPR), and engine control parameters such as engine bleed air commands, variable geometry vane commands and others. The monitored engine output data 111 comprises data pertaining to gas path parameters (GPP) such as fuel, flow, internal shaft speeds, compressor, combustor and turbine temperatures and pressures and others. The physics-based engine model 105 outputs estimated parameter data 113 corresponding to each engine output parameter 111.
The estimated parameter data 113 may be used for a variety of purposes. The parameter data 113 provide for analytical redundancy if a channel mismatch were to occur, for example, in a multichannel redundant system such as a Full Authority Digital Engine Control (FADEC) (not shown), serving as an auctioneer between two redundant signals that have different values.
The physics-based engine model 105 estimated output parameter data 113 are compared with the engine output parameter data 111 to form residuals 115. If the physics-based engine model 105 is an accurate representation of the monitored engine 103 and if the engine is performing under nominal conditions, the residuals 115 should be close to zero on the average. The residuals represent the difference between an actual engine output data 111 and the related engine model estimated output data 113. The magnitude of the residuals indicates the accuracy of the physics-based engine model 105. However, as the operating time of an engine increases beyond a certain point, its performance typically decreases and the residuals 115 deviate from zero.
The performance estimator 107 uses the residuals 115 to observe changes in performance across the engine's modules (e.g., compressor, combustor, turbine, etc.), in the form of adiabatic efficiencies, flow capacities, and turbine nozzle area deltas. This type of analysis is referred to as Gas Path Analysis (GPA) or Module Performance Analysis (MPA). The disparities between the physics-based engine model 105 and engine 103 outputs are used to modify the performance output of the engine model estimated outputs 113 to drive the residuals 115 to zero (on the average). In this manner, the physics-based engine model estimated outputs 113 more accurately reflect the current state of the engine 103 and the module performance deltas can be tracked over time to aid in determining proper engine work scope when the engine is removed for maintenance.
The model 101 described above and shown in FIG. 1 represents an ideal situation where the physics-based engine model 105 is a faithful representation of the engine 103 being monitored. However, the physics-based engine model 105 typically does not hold true in practice. Engine-to-engine variations, models simplified in order to save processing time, deviations caused by complicated improvements to the engine's hardware, bleed and stator vane schedules, cooling flows, handling bleeds, etc., over the engine's life cycle are not reflected in the model 105 and contribute to output disparities between the physics-based engine model 105 and engine 103. The disparities result in inaccurate estimations in the module performance tracking for the model 101 which can result in unnecessary engine maintenance or removals, etc. Due to the penalties and high costs associated with such events, this is undesirable for both engine manufacturers and airliners.
FIG. 2 illustrates an engine model 102 that is a variation of the model 101 shown in FIG. 1, wherein the input parameters 109 are stored in a database along with the residuals associated with those input parameters. This database is used for viewing the performance of the engine over a period of time. Once developed, output 116 from this database is used for empirical fine tuning of the physics-based engine model 105. Although this engine model 102 represents an improvement over the model 101 shown in FIG. 1, it can still be subject to data biases and correlations and therefore inaccurate.